Employing Magnetic Levitation To Monitor Reaction Kinetics and

Laboratory Experiment pubs.acs.org/jchemeduc

Employing Magnetic Levitation To Monitor Reaction Kinetics and Measure Activation Energy Lauren Benz,*,† Karen E. Cesafsky,† Tran Le,† Aileen Park,† and David Malicky‡ Departments of †Chemistry and Biochemistry and ‡Engineering, University of San Diego, California 92110, United States S Supporting Information *

ABSTRACT: This article describes a simple and inexpensive undergraduate-level kinetics experiment that uses magnetic levitation to monitor the progress and determine the activation energy of a condensation reaction on a polymeric solid support. The method employs a cuvette filled with a paramagnetic solution positioned between two strong magnets. The vertical position of the polymeric beads suspended in the paramagnetic solution correlates with the density of the beads and, consequently, with the progress of the chemical reaction within these beads. Varying the temperature of the reaction between the leucine-functionalized support and 2,5-diiodobenzoic acid under pseudo-first-order reaction conditions yields an activation energy of 65.4 ± 9.2 kJ/mol. This value compares well the activation energy of 63.5 ± 4.1 kJ/mol determined using a density analysis. This experiment combines a number of interdisciplinary concepts including organic chemistry, kinetics, and magnetism and, therefore, could be implemented in a number of undergraduate chemistry courses at various levels. KEYWORDS: Upper-Division Undergraduate, Interdisciplinary/Multidisciplinary, Laboratory Instruction, Organic Chemistry, Physical Chemistry, Hands-On Learning/Manipulatives, Amines/Ammonium Compounds, Kinetics, Magnetic Properties

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is described in greater detail elsewhere.10 Figure 1 shows a picture (left) of a diamagnetic nylon bead in a paramagnetic gadolinium chloride (GdCl3) solution. Because the density of nylon is 1.13 g/mL and the density of the solution is 1.10 g/mL, the bead sinks in the absence of a strong magnetic field due to the net force of gravity (or “buoyant force”). When the cuvette is placed between two NdFeB magnets (Figure 1, right), the magnetic field causes the bead to levitate! This phenomenon results primarily from the attraction of the paramagnetic solution toward the magnet and a corresponding displacement of the beads to a lower-field region between the magnets. Levitation height is related to the density of the object being levitated, such that change in density can translate into measurable change in position within a magnetic field.10 The magnets are arranged in an anti-Helmholtz configuration with like poles facing each other, resulting in a magnetic field that is greatest in magnitude at the magnet faces and weakest at the center point between the magnets. The magnetic moments of the paramagnetic Gd3+ ions align with the direction of the magnetic field lines when placed between the two magnets. Gd3+ ions have seven unpaired electrons, making the response to the magnetic field relatively strong. When the cuvette is placed in the magnetic field, an upward magnetic force cancels the downward net gravitational force on the bead at a certain

number of methods are used in the laboratory to monitor reaction kinetics. Spectrophotometry is frequently employed in homogeneous systems when one of the reactants or products absorbs light uniquely at a certain wavelength. It is often the tool of choice when introducing kinetics at the undergraduate level.1 If NMR is available, this can also be an invaluable tool for monitoring kinetics.2 Other methods include differential scanning calorimetry, which can be used in solid−solid reactions,3 and temperature programmed desorption, which is useful when studying gas−solid systems.4 All of the above methods require expensive and sophisticated equipment. Simpler methods such as titration in aqueous media1 can be time-consuming and, therefore, not amenable to incorporation into a laboratory curriculum. The use of magnetic levitation, described herein, is a time and cost-effective technique in the kinetic study of a heterogeneous reaction. Heterogeneous reaction systems gained early notoriety in the synthesis of peptides due to the ease with which excess reagent and unwanted side products could be rinsed off,5 and since then have become important in combinatorial chemistry and drug discovery.6 For such heterogeneous reactions, spectrophotometry7,8 and titration9 can be employed to monitor reaction kinetics similar to homogeneous systems; however, an additional cleavage step is often needed. In experiments described herein, a unique method is applied to probe the kinetics of reactions on diamagnetic solid supports that utilizes magnetic levitation. Levitation is briefly introduced here, and is also summarized in the Supporting Information. The physics of this phenomenon © 2012 American Chemical Society and Division of Chemical Education, Inc.

Published: April 6, 2012 776

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column (which contained a frit) on a vacuum manifold and washed (over vacuum). The columns were then capped and dried under vacuum. During the second lab period (minimum of 3 h), the deprotected resin was placed in 50 mL of DMF along with an 8-fold molar excess of the following (to establish pseudo-first-order conditions): 2,5-diiodibenzoic acid, O(benzotriazol-1-yl)-N,N,N′,N′-tetramethyluronium hexafluorophosphate (HBTU), and N,N-diisopropylethylamine (DIEA). The reaction was run at four temperatures: 273, 280, 285, and 294 K. Aliquots (∼5 mL) of the reaction mixture were withdrawn at appropriate times during the reaction (see the Supporting Information). The aliquots were transferred to small disposable chromatography columns, rinsed, and dried under vacuum. The beads were then suspended in cuvettes containing 590 mM GdCl3 in DMF and allowed to swell for at least 15 min. Students worked in groups of 2−3, with each group responsible for testing the kinetics of a particular temperature.

Figure 1. A nylon bead in a cuvette containing a GdCl3 solution. In the absence of a magnetic field (left), the bead sinks because its density is greater than that of the solution. The net force of gravity, Fg, is downward. When placed in the magnetic field, the bead levitates due to the upward magnetic force, Fb, that cancels the force of gravity at a certain point between the magnets.

Levitation Height Measurement

The experimental setup is shown in Figure 1 (right). Two strong (∼0.4 T) NdFeB magnets were positioned in the antiHelmholtz configuration, with similar poles facing each other. They can be permanently fixed or set into an adjustable frame. We opted for the latter (designed and assembled by Gaudreau Engineering, RI, $500) to allow for some flexibility at the outset, but the former is less expensive and can be self-made (see Supporting Information for a full supply list and detailed construction steps). A cuvette containing 590 mM GdCl3 in DMF and a visible clump of the polystyrene beads (approximately 2 mg) was placed onto the center of the lower magnet. The sample was allowed to stand until the beads were well-clustered and no longer moving (see Figure 2 for typical appearance).

point between the magnets, causing the bead to levitate at this position. The magnitude of the opposing magnetic force varies linearly between the upper and lower magnets when the magnets are placed ∼45 mm apart.10 The position of the bead therefore depends linearly on the density of the bead. Hence, if the density of the bead shown were to increase, the net force of gravity on the bead in solution would increase, and therefore, it would reside closer to the lower magnet than shown because a greater magnetic force would be required to oppose the increased gravitational force. This phenomenon was used to devise a simple and convenient undergraduate-level kinetics experiment to probe the reaction of a polystyrene resin-bound amino acid, leucine, with 2,5-diiodobenzoic acid, as a function of time and temperature. This method can be applied to a host of different chemical reactions on solid supports.11

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EXPERIMENTAL DETAILS

Reaction of Leucine-Functionalized Resin with 2,5-Diiodobenzoic Acid

The reaction probed in this experiment is shown in Scheme 1 and detailed instructions are given in the Supporting Information. Scheme 1. Reaction of the Leucine-Functionalized Resin

Figure 2. A sample levitation progression of a reaction run at 273 K. The bead clump moves toward the bottom of the cuvette over time as the beads become increasingly dense with product.

Levitation height was measured at the vertical center of the cluster with a millimeter-scaled ruler from the bottom of the magnet (set to 0). When the cluster was spread out, the center of mass was estimated by eye. This process was repeated using beads from the aliquots of the reaction mixture taken at different times and rinsed as mentioned above. Density Measurement Using a Sink−Float Analysis (Optional)

During the first lab period (minimum of 2 h), the N-(9fluorenylmethoxycarbonyl)-protected leucine-functionalized resin was deprotected by agitating the resin in a 25% (v/v) solution of piperidine in dimethylformamide (DMF). After deprotection, the resin was separated from the reaction mixture by pouring the solution into a large disposable chromatography

Approximately 20 aqueous CaCl2 solutions were prepared with densities ranging from 1.1400 to 1.3700 g/mL. A small quantity (1−2 mg) of the resin was suspended in several of these solutions and centrifuged at 9800g for 2 min. If the beads floated to 777

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the top of the vial or sank to the bottom, the density was less than or greater than that of the solution, respectively. If the beads were uniformly dispersed in the vial, the density matched that of the solution. This process was repeated using different densities of CaCl2 solution until the densities for all time points for a given reaction were determined. The solution densities were measured using a volumetric pipet and a balance. Students needed 2 h for this experiment.

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HAZARDS Goggles, a lab coat, and gloves are required for this experiment. All organic solvents should be used under a fume hood. Organic solvents used for rinsing were placed in wash bottles to minimize the risk of exposure, and students double gloved (nitrile under ethylene vinyl alcohol/polyethylene) while working with CH2Cl2. Be cautious while working with the magnets, keeping all magnetic metals away from the levitation device. It is important to rinse the magnets off with acetone or other suitable solvent after use to prevent corrosion from DMF. Refer to the MSDS for specific hazard information for all materials used in the experiment.

Figure 3. Plots of ln[−NH2] vs time used to determine kinetic parameters for the reaction of a leucine-functionalized resin with 2,5diiodobenzoic acid at 273, 280, 285, and 294 K. Correlation coefficient (R2) values ranged from 0.97 to 0.98.

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kinetics of the reaction when an excess of acid is used. All data points collected in at least three independent trials for each temperature are shown. A linear regression to the average of these points was plotted (solid lines). Pseudo-firstorder rate constants for the overall reaction were determined for the four temperatures and are given in Table 1. The rate

RESULTS AND DISCUSSION Photographs of an actual reaction progression (student data) run at 0 °C are shown in Figure 2. The cluster of beads starts at its highest position at 37 mm (lowest bead density is at time; 0 min) and as time progresses, the beads sink as they become more dense. The beads appear somewhat spread out in the cuvette in the middle of the reaction (∼20−30 min) likely due to the fact that the beads are polydisperse in size (∼75− 150 μm), altering the accessibility of the acid to the interior amines of the beads.11,12 To assess the kinetics of the reaction, the concentration of −NH2 on the beads at time zero was determined using the amine loading level and the density of the leucine-functionalized beads (provided by the manufacturer, Matrix Innovations), according to eq 1

Table 1. Comparison of the Experimental Rate Constants Using the Levitation and Sink−Float Methods Pseudo-First-Order Rate Constants/(10−3 s−1) Method

273 K

280 K

285 K

294 K

Levitation Sink−float

0.96 ± 0.13 1.05 ± 0.17

1.56 ± 0.18 2.18 ± 0.26

3.84 ± 0.10 3.96 ± 0.16

6.81 ± 1.27 7.55 ± 1.01

constants were used to find the activation energy from the Arrhenius relation, as plotted in Figure 4, which was

[−NH2]0%conversion ⎛ 0.72 mmol ⎞⎛ 1 mol ⎞⎛ 1.12 g ⎞⎛ 1000 cm3 ⎞ ⎟⎜ ⎟⎟ =⎜ ⎟⎜ ⎟⎜⎜ L g ⎝ ⎠⎝ 1000 mmol ⎠⎝ cm3 ⎠⎝ ⎠ = 0.81

mol L

(1)

Once this initial concentration is determined, the concentration at any time point during the experiment can be found using the levitation height, according to eq 2, where z represents the resin cluster’s measured height: [−NH2]experiment ⎛ zexperiment − z100%conversion ⎞ =⎜ ⎟ ⎝ z 0%conversion − z100%conversion ⎠ × [−NH2]0%conversion

Figure 4. Arrhenius plots from the levitation measurements (blue) and the sink−float measurements (red) yield activation energies of 65.4 ± 9.2 and 63.5 ± 4.1 kJ/mol, respectively. The reported error is the standard error in the slope of the average graph.

(2)

Further detail on eqs 1 and 2 is given in the Supporting Information. The reaction has reached 100% when the bead height reaches a minimum. A ninhydrin test can also be performed to confirm the completion of the coupling reaction. Linear plots of the natural log of the leucine concentration versus time at the four temperatures investigated are given in Figure 3 (student data), revealing the pseudo-first-order

determined to be 65.4 ± 9.2 kJ/mol using the levitation method. Errors of ±10−20% in the activation energy and rate constants obtained using the levitation method are comparable to those of similar reported kinetic data.1,13 To our knowledge, 778

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(2) Gallaher, T. N.; Gaul, D. A.; Schreiner, S. H. J. Chem. Educ. 1996, 73, 465−467. (3) Zhang, Y. X.; Vyazovkin, S. J. Phys. Chem. B 2007, 111, 7098−7104. (4) Du, Z.; Sarofim, A. F.; Longwell, J. P. Energy Fuels 1990, 4, 296−302. (5) Merrifield, R. B. J. Am. Chem. Soc. 1963, 85, 2149−2154. (6) Mendonca, A. J.; Xiao, X. Y. Med. Res. Rev. 1999, 19, 451−462. (7) Mazur, S.; Jayalekshmy, P. J. Am. Chem. Soc. 1978, 677−683. (8) Chu, S. S.; Reich, S. H. Bioorg. Med. Chem. Lett. 1995, 5, 1053− 1058. (9) Lu, G.-S.; Mosjov, S.; Tan, J. P.; Merrifield, R. B. J. Org. Chem. 1981, 46, 3433−3436. (10) Mirica, K. A.; Shevkoplyas, S. S.; Phillips, S. T.; Gupta, M.; Whitesides, G. M. J. Am. Chem. Soc. 2009, 131, 10049−10058. (11) Mirica, K. A.; Phillips, S. T.; Shevkoplyas, S. S.; Whitesides, G. M. J. Am. Chem. Soc. 2008, 130, 17678−17680. (12) Li, W. B.; Yan, B. J. Org. Chem. 1998, 63, 4092−4097. (13) Sattar, S. J. Chem. Educ. 2011, 88, 457−460. (14) Evmiridis, N. P.; Karayannis, M. I. Anal. Chim. Acta 1983, 151, 211−219.

there is no previously reported activation energy for this specific reaction; however, the related homogeneous reaction between L-leucine and trinitrobenzenesulfonic acid has been studied, and the reported activation energy of 53.6 kJ/mol is reasonably close to the value measured herein.14 Students also employed a sink−float method to track the kinetics of the reaction by measuring density changes of the beads over time. Because a linear relationship exists between the density and the levitation height,10 one expects to obtain similar results when using a sink−float method to assess the reaction kinetics. This is the case as shown by the comparison of rate constants in Table 1 (analogous plot to Figure 3 given in Supporting Information). The activation energy can also be determined from this data using the Arrhenius relation and plotting ln(k) versus 1/T (dotted line, Figure 4). With the use of the linear regression applied to the average rate constant of three trials and the standard error in the slope, the activation energy was found to be 63.5 ± 4.1 kJ/mol from the sink−float method. This value is in good agreement with the activation energy measured using the levitation method.

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SUMMARY Magnetic levitation is a unique and accessible method to probe kinetics and determine activation energies in reactions on solid supports. One advantage that this technique has over traditional spectrophotometric methods is that it is relatively inexpensive. It is also time-efficient and can be completed within one or two 4-h laboratory periods. Furthermore, as this method combines physics and chemistry, it can be used at various levels in the undergraduate laboratory curriculum. This experiment was developed and tested by four students as part of an upperdivision research methods course and general upper-division research at this university. The students were enthusiastic about the levitation method. As they had previously completed a spectrophotmetric kinetics module in general chemistry, this experiment helped reinforce and build upon their background by presenting a new and unique method to measure kinetic parameters.

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ASSOCIATED CONTENT

S Supporting Information *

Instructor notes; a student handout; and detailed instructions for the construction of the magnet holder. This material is available via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Joseph Salameh for his assistance, Katherine Mirica for her help in learning the reaction steps and insightful conversation, and Jeremy Kua, Christopher Daley, and Tammy Dwyer for valuable advice. Thanks to the University of San Diego for financial support through a Teaching and Learning Grant.

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REFERENCES

(1) Barile, R. C.; Michiels, L. P. J. Chem. Educ. 1983, 60, 154. 779

dx.doi.org/10.1021/ed2004577 | J. Chem. Educ. 2012, 89, 776−779